Find the coordinates on the unit circle at different angles

To find the coordinates on the unit circle at 45 degrees:

The unit circle equation is given by:

$x^2 + y^2 = 1$

For an angle of \(45^{\circ}\) or \(\frac{\pi}{4}\) radians, the coordinates are:

$x = \cos(\frac{\pi}{4})$

$y = \sin(\frac{\pi}{4})$

Both \(\cos(\frac{\pi}{4})\) and \(\sin(\frac{\pi}{4})\) are equal to \(\frac{\sqrt{2}}{2}\).

Hence, the coordinates are:

$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $.

To find the coordinates on the unit circle at 90 degrees:

The unit circle equation is:

$x^2 + y^2 = 1$

For an angle of (90^{circ}) or (frac{pi}{2}) radians, the coordinates are:

$x = cos(frac{pi}{2})$

$y = sin(frac{pi}{2})$

Since (cos(frac{pi}{2}) = 0) and (sin(frac{pi}{2}) = 1):

The coordinates are:

$ (0, 1) $.

To find the coordinates on the unit circle at 180 degrees:

The unit circle equation is:

$x^2 + y^2 = 1$

For an angle of (180^{circ}) or (pi) radians, the coordinates are:

$x = cos(pi)$

$y = sin(pi)$

Since (cos(pi) = -1) and (sin(pi) = 0):

The coordinates are:

$ (-1, 0) $.

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